Subgroups — C₇×#34424 #13211640

Order 1792.

2442 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#538	C₂	1	1	yes	maximal, characteristic
2	C₇×#2379	C₂	1	2	yes	maximal, complemented
3	C₇×#2376	C₂	1	2	yes	maximal, complemented
4	C₇×#2367	C₂	1	2	yes	maximal, complemented
5	C₇×#2359	C₂	1	2	yes	maximal, complemented
6	C₇×#2358	C₂	1	2	yes	maximal, complemented
7	C₇×#2358	C₂	1	2	yes	maximal, complemented
8	C₇×#2352	C₂	1	2	yes	maximal, complemented
9	C₇×#2349	C₂	1	2	yes	maximal, complemented
10	C₇×#2334	C₂	1	2	yes	maximal, complemented
11	C₇×#2334	C₂	1	2	yes	maximal, complemented
12	C₇×#2329	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#2325	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2325	C₂	1	2	yes	maximal, complemented
15	C₇×#2324	C₂	1	2	yes	maximal, complemented
16	C₇×#2315	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₇×#388	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#538	C₄	1	16	yes	complemented
21	C₂×C₇×#126	C₂²	1	2	yes	—
22	C₂×C₇×#124	C₂²	1	2	yes	—
23	C₂×C₇×#123	C₂²	1	2	yes	—
24	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×#121	C₂²	1	1	yes	characteristic
26	C₂×C₇×#121	C₂²	1	2	yes	—
27	C₂×C₇×#120	C₂²	1	2	yes	—
28	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
30	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
31	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
32	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
33	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
34	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₇×#117	C₂²	1	2	yes	complemented
36	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
40	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
42	C₇×#391	C₂²	1	1	yes	characteristic, complemented
43	C₇×#391	C₂²	1	2	yes	complemented
44	C₇×#390	C₂²	1	2	yes	—
45	C₇×#390	C₂²	1	2	yes	—
46	C₇×#390	C₂²	1	1	yes	characteristic, complemented
47	C₇×#389	C₂²	1	1	yes	characteristic, complemented
48	C₇×#389	C₂²	1	1	yes	characteristic, complemented
49	C₇×#389	C₂²	1	2	yes	complemented
50	C₇×#389	C₂²	1	2	yes	complemented
51	C₇×#389	C₂²	1	2	yes	complemented
52	C₇×#388	C₂²	1	2	yes	—
53	C₇×#388	C₂²	1	2	yes	—
54	C₇×#388	C₂²	1	2	yes	—
55	C₇×#388	C₂²	1	2	yes	—
56	C₇×#388	C₂²	1	2	yes	—
57	C₇×#388	C₂²	1	2	yes	—
58	C₇×#388	C₂²	1	2	yes	—
59	C₇×#388	C₂²	1	2	yes	—
60	C₇×#388	C₂²	1	2	yes	complemented
61	C₇×#388	C₂²	1	2	yes	complemented
62	C₇×#388	C₂²	1	2	yes	complemented
63	C₇×#388	C₂²	1	2	yes	complemented
64	C₇×#387	C₂²	1	2	yes	complemented
65	C₇×#387	C₂²	1	2	yes	complemented
66	C₇×#387	C₂²	1	2	yes	complemented
67	C₇×#387	C₂²	1	2	yes	complemented
68	C₇×#387	C₂²	1	2	yes	complemented
69	C₇×#387	C₂²	1	2	yes	complemented
70	C₇×#386	C₂²	1	2	yes	—
71	C₇×#386	C₂²	1	2	yes	—
72	C₇×#386	C₂²	1	2	yes	—
73	C₇×#386	C₂²	1	2	yes	—
74	C₇×#386	C₂²	1	2	yes	—
75	C₇×#386	C₂²	1	2	yes	—
76	C₇×#386	C₂²	1	2	yes	complemented
77	C₇×#385	C₂²	1	2	yes	—
78	C₇×#385	C₂²	1	2	yes	—
79	C₇×#385	C₂²	1	2	yes	—
80	C₇×#385	C₂²	1	2	yes	—
81	C₇×#385	C₂²	1	2	yes	—
82	C₇×#385	C₂²	1	2	yes	—
83	C₇×#385	C₂²	1	2	yes	—
84	C₇×#385	C₂²	1	2	yes	—
85	C₇×#385	C₂²	1	2	yes	complemented
86	C₇×#385	C₂²	1	2	yes	complemented
87	C₇×#385	C₂²	1	2	yes	complemented
88	C₇×#382	C₂²	1	2	yes	complemented
89	C₇×#382	C₂²	1	2	yes	complemented
90	C₇×#380	C₂²	1	1	yes	characteristic
91	C₇×#380	C₂²	1	1	yes	characteristic
92	C₇×#380	C₂²	1	2	yes	—
93	C₇×#380	C₂²	1	2	yes	complemented
94	C₇×#380	C₂²	1	2	yes	complemented
95	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
96	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
97	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
98	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
99	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
100	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
101	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
102	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
103	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
104	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
105	C₂×C₇×#95	C₂²	1	1	yes	characteristic
106	C₂×C₇×#95	C₂²	1	1	yes	characteristic
107	C₂×C₇×#95	C₂²	1	2	yes	complemented
108	#34424	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂⁵×C₇	C₂³	1	1	yes	characteristic
110	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
111	C₂²×C₇×D₄	C₂³	1	2	yes	—
112	C₂²×C₇×D₄	C₂³	1	2	yes	—
113	C₂²×C₇×D₄	C₂³	1	2	yes	—
114	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₇	C₂³	1	2	yes	—
120	C₂³×C₄×C₇	C₂³	1	2	yes	—
121	C₂³×C₄×C₇	C₂³	1	2	yes	—
122	C₂³×C₄×C₇	C₂³	1	2	yes	—
123	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₇	C₂³	1	2	yes	—
126	C₇×#126	C₂×C₄	1	16	yes	complemented
127	C₇×#124	C₂×C₄	1	16	yes	complemented
128	C₇×#123	C₂×C₄	1	16	yes	complemented
129	C₇×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
130	C₇×#121	C₂×C₄	1	16	yes	complemented
131	C₇×#121	C₂×C₄	1	8	yes	complemented
132	C₇×#120	C₂×C₄	1	16	yes	complemented
133	C₄×C₇×Q₈	—	4	2	no	—
134	C₄×C₇×D₄	—	4	4	no	—
135	C₄×C₇×D₄	—	4	2	no	—
136	C₄×C₇×D₄	—	4	4	no	—
137	C₄×C₇×D₄	—	4	4	no	—
138	C₄×C₇×D₄	—	4	4	no	—
139	C₄×C₇×D₄	C₂×C₄	1	16	yes	complemented
140	C₇×#117	—	4	4	no	—
141	C₂×C₇×C₄⋊C₄	—	4	2	no	—
142	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
161	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
162	C₂×C₇×C₂²⋊C₄	—	4	4	no	—
163	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
164	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₄²×C₇	—	4	2	no	—
186	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₇	C₂³	1	2	yes	—
189	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₇	C₂³	1	2	yes	—
192	C₂×C₄²×C₇	C₂³	1	2	yes	—
193	C₂×C₄²×C₇	C₂³	1	2	yes	—
194	C₂×C₄²×C₇	C₂³	1	2	yes	—
195	C₂×C₄²×C₇	C₂³	1	2	yes	—
196	C₂×C₄²×C₇	C₂³	1	2	yes	—
197	C₇×#95	C₂³	1	2	yes	—
198	C₇×#95	C₂³	1	2	yes	—
199	C₇×#95	C₂³	1	2	yes	—
200	C₇×#95	C₂³	1	2	yes	—
201	C₇×#95	C₂³	1	2	yes	—
202	C₇×#95	C₂³	1	2	yes	—
203	C₇×#95	C₂³	1	2	yes	—
204	C₇×#95	C₂³	1	2	yes	—
205	C₇×#95	C₂³	1	2	yes	—
206	C₇×#95	C₂³	1	2	yes	—
207	C₇×#95	C₂³	1	2	yes	—
208	C₇×#95	C₂³	1	2	yes	—
209	C₇×#95	C₂³	1	2	yes	—
210	C₇×#95	C₂³	1	2	yes	—
211	C₇×#95	C₂³	1	2	yes	—
212	C₇×#95	C₂³	1	2	yes	—
213	C₇×#95	C₂³	1	2	yes	—
214	C₇×#95	C₂³	1	2	yes	—
215	C₇×#95	C₂³	1	2	yes	—
216	C₇×#95	C₂³	1	2	yes	—
217	C₂×#538	C₂×C₇	1	1	yes	characteristic
218	#2379	C₂×C₇	1	2	yes	complemented
219	#2376	C₂×C₇	1	2	yes	complemented
220	#2367	C₂×C₇	1	2	yes	complemented
221	#2359	C₂×C₇	1	2	yes	complemented
222	#2358	C₂×C₇	1	2	yes	complemented
223	#2358	C₂×C₇	1	2	yes	complemented
224	#2352	C₂×C₇	1	2	yes	complemented
225	#2349	C₂×C₇	1	2	yes	complemented
226	#2334	C₂×C₇	1	2	yes	complemented
227	#2334	C₂×C₇	1	2	yes	complemented
228	#2329	C₂×C₇	1	1	yes	characteristic, complemented
229	#2325	C₂×C₇	1	1	yes	characteristic, complemented
230	#2325	C₂×C₇	1	2	yes	complemented
231	#2324	C₂×C₇	1	2	yes	complemented
232	#2315	C₂×C₇	1	1	yes	characteristic, complemented
233	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
234	C₄×#121	C₂×C₇	1	1	yes	characteristic, complemented
235	C₂×#388	C₂×C₇	1	1	yes	characteristic, complemented
236	C₂⁴×C₇	—	2	2	no	—
237	C₂⁴×C₇	—	2	2	no	—
238	C₂⁴×C₇	—	4	1	no	—
239	C₂⁴×C₇	—	4	1	no	—
240	C₂⁴×C₇	—	4	1	no	—
241	C₂⁴×C₇	—	4	1	no	—
242	C₂⁴×C₇	C₂²×C₄	1	4	yes	—
243	C₂⁴×C₇	C₂⁴	1	2	yes	—
244	C₂⁴×C₇	C₂⁴	1	2	yes	—
245	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
246	C₂×C₇×Q₈	—	4	1	no	—
247	C₂×C₇×Q₈	—	4	1	no	—
248	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
249	C₂×C₇×D₄	—	2	4	no	—
250	C₂×C₇×D₄	—	2	4	no	—
251	C₂×C₇×D₄	—	4	2	no	—
252	C₂×C₇×D₄	—	4	1	no	—
253	C₂×C₇×D₄	—	4	2	no	—
254	C₂×C₇×D₄	—	4	2	no	—
255	C₂×C₇×D₄	—	4	1	no	—
256	C₂×C₇×D₄	—	4	2	no	—
257	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
258	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
259	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
260	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
261	C₂²×C₄×C₇	—	2	2	no	—
262	C₂²×C₄×C₇	—	2	2	no	—
263	C₂²×C₄×C₇	—	2	2	no	—
264	C₂²×C₄×C₇	—	2	2	no	—
265	C₂²×C₄×C₇	—	2	2	no	—
266	C₂²×C₄×C₇	—	2	2	no	—
267	C₂²×C₄×C₇	—	2	4	no	—
268	C₂²×C₄×C₇	—	4	1	no	—
269	C₂²×C₄×C₇	—	4	1	no	—
270	C₂²×C₄×C₇	—	4	1	no	—
271	C₂²×C₄×C₇	—	4	2	no	—
272	C₂²×C₄×C₇	—	4	1	no	—
273	C₂²×C₄×C₇	—	4	2	no	—
274	C₂²×C₄×C₇	—	4	1	no	—
275	C₂²×C₄×C₇	—	4	1	no	—
276	C₂²×C₄×C₇	—	4	1	no	—
277	C₂²×C₄×C₇	—	4	2	no	—
278	C₂²×C₄×C₇	—	4	2	no	—
279	C₂²×C₄×C₇	—	4	1	no	—
280	C₂²×C₄×C₇	—	4	1	no	—
281	C₂²×C₄×C₇	—	4	2	no	—
282	C₂²×C₄×C₇	—	4	2	no	—
283	C₂²×C₄×C₇	—	4	2	no	—
284	C₂²×C₄×C₇	—	4	2	no	—
285	C₂²×C₄×C₇	—	4	2	no	—
286	C₂²×C₄×C₇	—	4	2	no	—
287	C₂²×C₄×C₇	—	4	2	no	—
288	C₂²×C₄×C₇	—	4	2	no	—
289	C₂²×C₄×C₇	—	4	1	no	—
290	C₂²×C₄×C₇	—	4	2	no	—
291	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
292	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
293	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	—
294	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
310	C₇×C₄⋊C₄	—	2	4	no	—
311	C₇×C₄⋊C₄	—	2	4	no	—
312	C₇×C₄⋊C₄	—	4	2	no	—
313	C₇×C₄⋊C₄	—	4	2	no	—
314	C₇×C₄⋊C₄	—	4	1	no	—
315	C₇×C₄⋊C₄	—	4	2	no	—
316	C₇×C₄⋊C₄	—	4	1	no	—
317	C₇×C₄⋊C₄	—	4	2	no	—
318	C₇×C₄⋊C₄	—	4	2	no	—
319	C₇×C₄⋊C₄	—	4	2	no	—
320	C₇×C₄⋊C₄	—	4	1	no	—
321	C₇×C₄⋊C₄	—	4	2	no	—
322	C₇×C₄⋊C₄	—	4	2	no	—
323	C₇×C₄⋊C₄	—	4	1	no	—
324	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
325	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
326	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
327	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
328	C₇×C₂²⋊C₄	—	2	4	no	—
329	C₇×C₂²⋊C₄	—	2	4	no	—
330	C₇×C₂²⋊C₄	—	2	4	no	—
331	C₇×C₂²⋊C₄	—	2	4	no	—
332	C₇×C₂²⋊C₄	—	2	4	no	—
333	C₇×C₂²⋊C₄	—	4	2	no	—
334	C₇×C₂²⋊C₄	—	4	2	no	—
335	C₇×C₂²⋊C₄	—	4	2	no	—
336	C₇×C₂²⋊C₄	—	4	2	no	—
337	C₇×C₂²⋊C₄	—	4	2	no	—
338	C₇×C₂²⋊C₄	—	4	2	no	—
339	C₇×C₂²⋊C₄	—	4	2	no	—
340	C₇×C₂²⋊C₄	—	4	2	no	—
341	C₇×C₂²⋊C₄	—	4	2	no	—
342	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
343	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
344	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
345	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
346	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
347	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
348	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
349	C₄²×C₇	—	2	2	no	—
350	C₄²×C₇	—	2	2	no	—
351	C₄²×C₇	—	2	4	no	—
352	C₄²×C₇	—	4	1	no	—
353	C₄²×C₇	—	4	1	no	—
354	C₄²×C₇	—	4	2	no	—
355	C₄²×C₇	—	4	2	no	—
356	C₄²×C₇	—	4	2	no	—
357	C₄²×C₇	—	4	2	no	—
358	C₄²×C₇	—	4	2	no	—
359	C₄²×C₇	C₂²×C₄	1	8	yes	—
360	#538	C₄×C₇	1	16	yes	complemented
361	C₂×#126	C₂²×C₇	1	2	yes	—
362	C₂×#124	C₂²×C₇	1	2	yes	—
363	C₂×#123	C₂²×C₇	1	2	yes	—
364	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
365	C₂×#121	C₂²×C₇	1	2	yes	—
366	C₂×#121	C₂²×C₇	1	1	yes	characteristic
367	C₂×#120	C₂²×C₇	1	2	yes	—
368	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
369	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
370	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
371	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
372	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
373	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
374	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
375	C₂×#117	C₂²×C₇	1	2	yes	complemented
376	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
377	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
378	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
379	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
380	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
381	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
382	#391	C₂²×C₇	1	2	yes	complemented
383	#391	C₂²×C₇	1	1	yes	characteristic, complemented
384	#390	C₂²×C₇	1	2	yes	—
385	#390	C₂²×C₇	1	2	yes	—
386	#390	C₂²×C₇	1	1	yes	characteristic, complemented
387	#389	C₂²×C₇	1	2	yes	complemented
388	#389	C₂²×C₇	1	1	yes	characteristic, complemented
389	#389	C₂²×C₇	1	2	yes	complemented
390	#389	C₂²×C₇	1	2	yes	complemented
391	#389	C₂²×C₇	1	1	yes	characteristic, complemented
392	#388	C₂²×C₇	1	2	yes	—
393	#388	C₂²×C₇	1	2	yes	—
394	#388	C₂²×C₇	1	2	yes	—
395	#388	C₂²×C₇	1	2	yes	—
396	#388	C₂²×C₇	1	2	yes	—
397	#388	C₂²×C₇	1	2	yes	—
398	#388	C₂²×C₇	1	2	yes	—
399	#388	C₂²×C₇	1	2	yes	—
400	#388	C₂²×C₇	1	2	yes	complemented
401	#388	C₂²×C₇	1	2	yes	complemented
402	#388	C₂²×C₇	1	2	yes	complemented
403	#388	C₂²×C₇	1	2	yes	complemented
404	#387	C₂²×C₇	1	2	yes	complemented
405	#387	C₂²×C₇	1	2	yes	complemented
406	#387	C₂²×C₇	1	2	yes	complemented
407	#387	C₂²×C₇	1	2	yes	complemented
408	#387	C₂²×C₇	1	2	yes	complemented
409	#387	C₂²×C₇	1	2	yes	complemented
410	#386	C₂²×C₇	1	2	yes	—
411	#386	C₂²×C₇	1	2	yes	—
412	#386	C₂²×C₇	1	2	yes	—
413	#386	C₂²×C₇	1	2	yes	—
414	#386	C₂²×C₇	1	2	yes	—
415	#386	C₂²×C₇	1	2	yes	—
416	#386	C₂²×C₇	1	2	yes	complemented
417	#385	C₂²×C₇	1	2	yes	—
418	#385	C₂²×C₇	1	2	yes	—
419	#385	C₂²×C₇	1	2	yes	—
420	#385	C₂²×C₇	1	2	yes	—
421	#385	C₂²×C₇	1	2	yes	—
422	#385	C₂²×C₇	1	2	yes	—
423	#385	C₂²×C₇	1	2	yes	—
424	#385	C₂²×C₇	1	2	yes	—
425	#385	C₂²×C₇	1	2	yes	complemented
426	#385	C₂²×C₇	1	2	yes	complemented
427	#385	C₂²×C₇	1	2	yes	complemented
428	#382	C₂²×C₇	1	2	yes	complemented
429	#382	C₂²×C₇	1	2	yes	complemented
430	#380	C₂²×C₇	1	1	yes	characteristic
431	#380	C₂²×C₇	1	1	yes	characteristic
432	#380	C₂²×C₇	1	2	yes	—
433	#380	C₂²×C₇	1	2	yes	complemented
434	#380	C₂²×C₇	1	2	yes	complemented
435	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
436	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
437	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
438	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
439	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
440	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
441	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
442	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
443	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
444	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
445	C₂×#95	C₂²×C₇	1	1	yes	characteristic
446	C₂×#95	C₂²×C₇	1	1	yes	characteristic
447	C₂×#95	C₂²×C₇	1	2	yes	complemented
448	C₂³×C₇	—	2	1	no	—
449	C₂³×C₇	—	2	1	no	—
450	C₂³×C₇	—	2	1	no	—
451	C₂³×C₇	—	2	1	no	—
452	C₂³×C₇	—	2	2	no	—
453	C₂³×C₇	—	2	2	no	—
454	C₂³×C₇	—	2	2	no	—
455	C₂³×C₇	—	2	2	no	—
456	C₂³×C₇	—	2	2	no	—
457	C₂³×C₇	—	2	2	no	—
458	C₂³×C₇	—	2	2	no	—
459	C₂³×C₇	—	2	2	no	—
460	C₂³×C₇	—	2	2	no	—
461	C₂³×C₇	—	2	2	no	—
462	C₂³×C₇	—	2	2	no	—
463	C₂³×C₇	—	2	2	no	—
464	C₂³×C₇	—	2	8	no	—
465	C₂³×C₇	—	4	4	no	—
466	C₂³×C₇	—	4	4	no	—
467	C₂³×C₇	—	8	2	no	—
468	C₂³×C₇	—	8	2	no	—
469	C₂³×C₇	—	8	2	no	—
470	C₂³×C₇	—	8	2	no	—
471	C₂³×C₇	C₂³×C₄	1	4	yes	—
472	C₂³×C₇	C₂³×C₄	1	4	yes	—
473	C₂³×C₇	C₂³×C₄	1	2	yes	—
474	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
475	C₂³×C₇	2₋¹⁺⁴	1	2	yes	—
476	C₂³×C₇	C₂⁵	1	1	yes	characteristic
477	C₇×Q₈	—	4	4	no	—
478	C₇×D₄	—	2	16	no	—
479	C₇×D₄	—	4	8	no	—
480	C₇×D₄	—	4	4	no	—
481	C₇×D₄	—	4	8	no	—
482	C₂×C₄×C₇	—	2	1	no	—
483	C₂×C₄×C₇	—	2	1	no	—
484	C₂×C₄×C₇	—	2	2	no	—
485	C₂×C₄×C₇	—	2	1	no	—
486	C₂×C₄×C₇	—	2	2	no	—
487	C₂×C₄×C₇	—	2	2	no	—
488	C₂×C₄×C₇	—	2	1	no	—
489	C₂×C₄×C₇	—	2	2	no	—
490	C₂×C₄×C₇	—	2	1	no	—
491	C₂×C₄×C₇	—	2	2	no	—
492	C₂×C₄×C₇	—	2	2	no	—
493	C₂×C₄×C₇	—	2	2	no	—
494	C₂×C₄×C₇	—	2	1	no	—
495	C₂×C₄×C₇	—	2	1	no	—
496	C₂×C₄×C₇	—	2	2	no	—
497	C₂×C₄×C₇	—	2	1	no	—
498	C₂×C₄×C₇	—	2	1	no	—
499	C₂×C₄×C₇	—	2	2	no	—
500	C₂×C₄×C₇	—	2	1	no	—
501	C₂×C₄×C₇	—	2	2	no	—
502	C₂×C₄×C₇	—	2	2	no	—
503	C₂×C₄×C₇	—	2	2	no	—
504	C₂×C₄×C₇	—	2	2	no	—
505	C₂×C₄×C₇	—	2	2	no	—
506	C₂×C₄×C₇	—	2	2	no	—
507	C₂×C₄×C₇	—	2	2	no	—
508	C₂×C₄×C₇	—	2	2	no	—
509	C₂×C₄×C₇	—	2	2	no	—
510	C₂×C₄×C₇	—	2	2	no	—
511	C₂×C₄×C₇	—	2	2	no	—
512	C₂×C₄×C₇	—	2	1	no	—
513	C₂×C₄×C₇	—	2	1	no	—
514	C₂×C₄×C₇	—	2	1	no	—
515	C₂×C₄×C₇	—	2	2	no	—
516	C₂×C₄×C₇	—	2	1	no	—
517	C₂×C₄×C₇	—	2	2	no	—
518	C₂×C₄×C₇	—	2	2	no	—
519	C₂×C₄×C₇	—	2	2	no	—
520	C₂×C₄×C₇	—	2	2	no	—
521	C₂×C₄×C₇	—	2	2	no	—
522	C₂×C₄×C₇	—	4	4	no	—
523	C₂×C₄×C₇	—	4	8	no	—
524	C₂×C₄×C₇	—	4	4	no	—
525	C₂×C₄×C₇	—	4	4	no	—
526	C₂×C₄×C₇	—	4	4	no	—
527	C₂×C₄×C₇	—	8	4	no	—
528	C₂×C₄×C₇	—	8	2	no	—
529	C₂×C₄×C₇	—	8	2	no	—
530	C₂×C₄×C₇	—	8	4	no	—
531	C₂×C₄×C₇	—	8	4	no	—
532	C₂×C₄×C₇	—	8	4	no	—
533	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
534	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
535	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
536	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
537	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
538	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
539	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
540	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
541	C₂⁵	C₂³×C₇	1	1	yes	characteristic
542	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
543	C₂²×D₄	C₂³×C₇	1	2	yes	—
544	C₂²×D₄	C₂³×C₇	1	2	yes	—
545	C₂²×D₄	C₂³×C₇	1	2	yes	—
546	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
547	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
548	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
549	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
550	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
551	C₂³×C₄	C₂³×C₇	1	2	yes	—
552	C₂³×C₄	C₂³×C₇	1	2	yes	—
553	C₂³×C₄	C₂³×C₇	1	2	yes	—
554	C₂³×C₄	C₂³×C₇	1	2	yes	—
555	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
556	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
557	C₂³×C₄	C₂³×C₇	1	2	yes	—
558	#126	C₂×C₄×C₇	1	16	yes	complemented
559	#124	C₂×C₄×C₇	1	16	yes	complemented
560	#123	C₂×C₄×C₇	1	16	yes	complemented
561	C₂²⋊Q₈	C₂×C₄×C₇	1	8	yes	complemented
562	#121	C₂×C₄×C₇	1	16	yes	complemented
563	#121	C₂×C₄×C₇	1	8	yes	complemented
564	#120	C₂×C₄×C₇	1	16	yes	complemented
565	C₄×Q₈	—	4	2	no	—
566	C₄×D₄	—	4	4	no	—
567	C₄×D₄	—	4	2	no	—
568	C₄×D₄	—	4	4	no	—
569	C₄×D₄	—	4	4	no	—
570	C₄×D₄	—	4	4	no	—
571	C₄×D₄	C₂×C₄×C₇	1	16	yes	complemented
572	#117	—	4	4	no	—
573	C₂×C₄⋊C₄	—	4	2	no	—
574	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
592	C₂×C₂²⋊C₄	—	4	2	no	—
593	C₂×C₂²⋊C₄	—	4	2	no	—
594	C₂×C₂²⋊C₄	—	4	4	no	—
595	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	8	yes	complemented
596	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
617	C₂×C₄²	—	4	2	no	—
618	C₂×C₄²	C₂³×C₇	1	2	yes	—
619	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
620	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₇	1	2	yes	—
622	C₂×C₄²	C₂³×C₇	1	2	yes	—
623	C₂×C₄²	C₂³×C₇	1	2	yes	—
624	C₂×C₄²	C₂³×C₇	1	2	yes	—
625	C₂×C₄²	C₂³×C₇	1	2	yes	—
626	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₇	1	2	yes	—
629	#95	C₂³×C₇	1	2	yes	—
630	#95	C₂³×C₇	1	2	yes	—
631	#95	C₂³×C₇	1	2	yes	—
632	#95	C₂³×C₇	1	2	yes	—
633	#95	C₂³×C₇	1	2	yes	—
634	#95	C₂³×C₇	1	2	yes	—
635	#95	C₂³×C₇	1	2	yes	—
636	#95	C₂³×C₇	1	2	yes	—
637	#95	C₂³×C₇	1	2	yes	—
638	#95	C₂³×C₇	1	2	yes	—
639	#95	C₂³×C₇	1	2	yes	—
640	#95	C₂³×C₇	1	2	yes	—
641	#95	C₂³×C₇	1	2	yes	—
642	#95	C₂³×C₇	1	2	yes	—
643	#95	C₂³×C₇	1	2	yes	—
644	#95	C₂³×C₇	1	2	yes	—
645	#95	C₂³×C₇	1	2	yes	—
646	#95	C₂³×C₇	1	2	yes	—
647	#95	C₂³×C₇	1	2	yes	—
648	#95	C₂³×C₇	1	2	yes	—
649	C₂²×C₇	—	2	2	no	—
650	C₂²×C₇	—	2	2	no	—
651	C₂²×C₇	—	2	2	no	—
652	C₂²×C₇	—	2	2	no	—
653	C₂²×C₇	—	2	2	no	—
654	C₂²×C₇	—	2	2	no	—
655	C₂²×C₇	—	2	4	no	—
656	C₂²×C₇	—	2	4	no	—
657	C₂²×C₇	—	2	4	no	—
658	C₂²×C₇	—	2	4	no	—
659	C₂²×C₇	—	2	4	no	—
660	C₂²×C₇	—	2	4	no	—
661	C₂²×C₇	—	4	2	no	—
662	C₂²×C₇	—	4	2	no	—
663	C₂²×C₇	—	4	2	no	—
664	C₂²×C₇	—	4	2	no	—
665	C₂²×C₇	—	4	2	no	—
666	C₂²×C₇	—	4	2	no	—
667	C₂²×C₇	—	4	2	no	—
668	C₂²×C₇	—	4	2	no	—
669	C₂²×C₇	—	8	8	no	—
670	C₂²×C₇	#520	1	4	yes	—
671	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
672	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
673	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
674	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
675	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
676	C₂²×C₇	#585	1	1	yes	characteristic
677	C₂²×C₇	#585	1	1	yes	characteristic
678	C₄×C₇	—	2	4	no	—
679	C₄×C₇	—	2	4	no	—
680	C₄×C₇	—	2	4	no	—
681	C₄×C₇	—	2	2	no	—
682	C₄×C₇	—	2	2	no	—
683	C₄×C₇	—	2	4	no	—
684	C₄×C₇	—	2	2	no	—
685	C₄×C₇	—	2	2	no	—
686	C₄×C₇	—	4	1	no	—
687	C₄×C₇	—	4	2	no	—
688	C₄×C₇	—	4	2	no	—
689	C₄×C₇	—	4	1	no	—
690	C₄×C₇	—	4	2	no	—
691	C₄×C₇	—	4	2	no	—
692	C₄×C₇	—	4	2	no	—
693	C₄×C₇	—	4	2	no	—
694	C₂⁴	—	2	2	no	—
695	C₂⁴	—	2	2	no	—
696	C₂⁴	—	4	1	no	—
697	C₂⁴	—	4	1	no	—
698	C₂⁴	—	4	1	no	—
699	C₂⁴	—	4	1	no	—
700	C₂⁴	C₂²×C₄×C₇	1	4	yes	—
701	C₂⁴	C₂⁴×C₇	1	2	yes	—
702	C₂⁴	C₂⁴×C₇	1	2	yes	—
703	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
704	C₂×Q₈	—	4	1	no	—
705	C₂×Q₈	—	4	1	no	—
706	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
707	C₂×D₄	—	2	4	no	—
708	C₂×D₄	—	2	4	no	—
709	C₂×D₄	—	4	2	no	—
710	C₂×D₄	—	4	1	no	—
711	C₂×D₄	—	4	2	no	—
712	C₂×D₄	—	4	2	no	—
713	C₂×D₄	—	4	1	no	—
714	C₂×D₄	—	4	2	no	—
715	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
716	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
717	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
718	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	—	2	4	no	—
726	C₂²×C₄	—	4	1	no	—
727	C₂²×C₄	—	4	1	no	—
728	C₂²×C₄	—	4	1	no	—
729	C₂²×C₄	—	4	2	no	—
730	C₂²×C₄	—	4	1	no	—
731	C₂²×C₄	—	4	2	no	—
732	C₂²×C₄	—	4	1	no	—
733	C₂²×C₄	—	4	1	no	—
734	C₂²×C₄	—	4	1	no	—
735	C₂²×C₄	—	4	2	no	—
736	C₂²×C₄	—	4	2	no	—
737	C₂²×C₄	—	4	1	no	—
738	C₂²×C₄	—	4	1	no	—
739	C₂²×C₄	—	4	2	no	—
740	C₂²×C₄	—	4	2	no	—
741	C₂²×C₄	—	4	2	no	—
742	C₂²×C₄	—	4	2	no	—
743	C₂²×C₄	—	4	2	no	—
744	C₂²×C₄	—	4	2	no	—
745	C₂²×C₄	—	4	2	no	—
746	C₂²×C₄	—	4	2	no	—
747	C₂²×C₄	—	4	1	no	—
748	C₂²×C₄	—	4	2	no	—
749	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
750	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
751	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	—
752	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
753	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
754	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
756	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
757	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
758	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
759	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
760	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
763	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
765	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
768	C₄⋊C₄	—	2	4	no	—
769	C₄⋊C₄	—	2	4	no	—
770	C₄⋊C₄	—	4	2	no	—
771	C₄⋊C₄	—	4	2	no	—
772	C₄⋊C₄	—	4	2	no	—
773	C₄⋊C₄	—	4	1	no	—
774	C₄⋊C₄	—	4	2	no	—
775	C₄⋊C₄	—	4	2	no	—
776	C₄⋊C₄	—	4	1	no	—
777	C₄⋊C₄	—	4	2	no	—
778	C₄⋊C₄	—	4	1	no	—
779	C₄⋊C₄	—	4	2	no	—
780	C₄⋊C₄	—	4	1	no	—
781	C₄⋊C₄	—	4	2	no	—
782	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
783	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
784	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
785	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	—	2	4	no	—
790	C₂²⋊C₄	—	2	4	no	—
791	C₂²⋊C₄	—	4	2	no	—
792	C₂²⋊C₄	—	4	2	no	—
793	C₂²⋊C₄	—	4	2	no	—
794	C₂²⋊C₄	—	4	2	no	—
795	C₂²⋊C₄	—	4	2	no	—
796	C₂²⋊C₄	—	4	2	no	—
797	C₂²⋊C₄	—	4	2	no	—
798	C₂²⋊C₄	—	4	2	no	—
799	C₂²⋊C₄	—	4	2	no	—
800	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
801	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
802	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
803	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
804	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
805	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
806	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
807	C₄²	—	2	2	no	—
808	C₄²	—	2	2	no	—
809	C₄²	—	2	4	no	—
810	C₄²	—	4	1	no	—
811	C₄²	—	4	1	no	—
812	C₄²	—	4	2	no	—
813	C₄²	—	4	2	no	—
814	C₄²	—	4	2	no	—
815	C₄²	—	4	2	no	—
816	C₄²	—	4	2	no	—
817	C₄²	C₂²×C₄×C₇	1	8	yes	—
818	C₂×C₇	—	2	4	no	—
819	C₂×C₇	—	4	4	no	—
820	C₂×C₇	—	4	4	no	—
821	C₂×C₇	C₂×#520	1	1	yes	characteristic
822	C₂×C₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
823	C₂×C₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
824	C₂×C₇	#3534	1	1	yes	characteristic
825	C₂×C₇	#3536	1	1	yes	characteristic
826	C₂×C₇	#3558	1	1	yes	characteristic
827	C₂×C₇	#3564	1	1	yes	characteristic
828	C₂³	—	2	1	no	—
829	C₂³	—	2	1	no	—
830	C₂³	—	2	1	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	2	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	2	no	—
837	C₂³	—	2	2	no	—
838	C₂³	—	2	2	no	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	2	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	8	no	—
845	C₂³	—	4	4	no	—
846	C₂³	—	4	4	no	—
847	C₂³	—	8	2	no	—
848	C₂³	—	8	2	no	—
849	C₂³	—	8	2	no	—
850	C₂³	—	8	2	no	—
851	C₂³	C₂³×C₄×C₇	1	4	yes	—
852	C₂³	C₂³×C₄×C₇	1	4	yes	—
853	C₂³	C₂³×C₄×C₇	1	2	yes	—
854	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
855	C₂³	C₇×2₋¹⁺⁴	1	2	yes	—
856	C₂³	C₂⁵×C₇	1	1	yes	characteristic
857	Q₈	—	4	4	no	—
858	D₄	—	2	16	no	—
859	D₄	—	4	8	no	—
860	D₄	—	4	4	no	—
861	D₄	—	4	8	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	4	4	no	—
903	C₂×C₄	—	4	8	no	—
904	C₂×C₄	—	4	4	no	—
905	C₂×C₄	—	4	4	no	—
906	C₂×C₄	—	4	4	no	—
907	C₂×C₄	—	8	4	no	—
908	C₂×C₄	—	8	2	no	—
909	C₂×C₄	—	8	2	no	—
910	C₂×C₄	—	8	4	no	—
911	C₂×C₄	—	8	4	no	—
912	C₂×C₄	—	8	4	no	—
913	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
914	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
915	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
916	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
917	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
918	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
919	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
920	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
921	C₇	#34424	1	1	yes	characteristic, direct product factor, Sylow
922	C₂²	—	2	2	no	—
923	C₂²	—	2	2	no	—
924	C₂²	—	2	2	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	2	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	4	no	—
929	C₂²	—	2	4	no	—
930	C₂²	—	2	4	no	—
931	C₂²	—	2	4	no	—
932	C₂²	—	2	4	no	—
933	C₂²	—	2	4	no	—
934	C₂²	—	4	2	no	—
935	C₂²	—	4	2	no	—
936	C₂²	—	4	2	no	—
937	C₂²	—	4	2	no	—
938	C₂²	—	4	2	no	—
939	C₂²	—	4	2	no	—
940	C₂²	—	4	2	no	—
941	C₂²	—	4	2	no	—
942	C₂²	—	8	8	no	—
943	C₂²	C₇×#520	1	4	yes	—
944	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
945	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
946	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
947	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
948	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
949	C₂²	C₇×#585	1	1	yes	characteristic
950	C₂²	C₇×#585	1	1	yes	characteristic
951	C₄	—	2	4	no	—
952	C₄	—	2	4	no	—
953	C₄	—	2	4	no	—
954	C₄	—	2	2	no	—
955	C₄	—	2	2	no	—
956	C₄	—	2	4	no	—
957	C₄	—	2	2	no	—
958	C₄	—	2	2	no	—
959	C₄	—	4	1	no	—
960	C₄	—	4	2	no	—
961	C₄	—	4	2	no	—
962	C₄	—	4	1	no	—
963	C₄	—	4	2	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	2	no	—
967	C₂	—	2	4	no	—
968	C₂	—	4	4	no	—
969	C₂	—	4	4	no	—
970	C₂	C₂×C₇×#520	1	1	yes	characteristic
971	C₂	C₄×C₇×H(5,𝔽₂)	1	1	yes	characteristic
972	C₂	C₄×C₇×H(5,𝔽₂)	1	1	yes	characteristic
973	C₂	C₇×#3534	1	1	yes	characteristic
974	C₂	C₇×#3536	1	1	yes	characteristic
975	C₂	C₇×#3558	1	1	yes	characteristic
976	C₂	C₇×#3564	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₇
Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂×C₇×#538	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₇×#2379	C₂	semidirect
3. C₇×#2376	C₂	semidirect
4. C₇×#2367	C₂	semidirect
5. C₇×#2359	C₂	semidirect
6. C₇×#2358	C₂	semidirect
7. C₇×#2358	C₂	semidirect
8. C₇×#2352	C₂	semidirect
9. C₇×#2349	C₂	semidirect
10. C₇×#2334	C₂	semidirect
11. C₇×#2334	C₂	semidirect
12. C₇×#2329	C₂	semidirect
13. C₇×#2325	C₂	semidirect
14. C₇×#2325	C₂	semidirect
15. C₇×#2324	C₂	semidirect
16. C₇×#2315	C₂	semidirect
17. C₄×C₇×C₂²⋊Q₈	C₂	semidirect
18. C₄×C₇×#121	C₂	semidirect
19. C₂×C₇×#388	C₂	semidirect
20. C₇×#538	C₄	semidirect
28. C₂×C₄×C₇×Q₈	C₂²	semidirect
34. C₂×C₄×C₇×D₄	C₂²	semidirect
35. C₂×C₇×#117	C₂²	semidirect
42. C₇×#391	C₂²	semidirect
43. C₇×#391	C₂²	semidirect
46. C₇×#390	C₂²	semidirect
47. C₇×#389	C₂²	semidirect
48. C₇×#389	C₂²	semidirect
49. C₇×#389	C₂²	semidirect
50. C₇×#389	C₂²	semidirect
51. C₇×#389	C₂²	semidirect
60. C₇×#388	C₂²	semidirect
61. C₇×#388	C₂²	semidirect
62. C₇×#388	C₂²	semidirect
63. C₇×#388	C₂²	semidirect
64. C₇×#387	C₂²	semidirect
65. C₇×#387	C₂²	semidirect
66. C₇×#387	C₂²	semidirect
67. C₇×#387	C₂²	semidirect
68. C₇×#387	C₂²	semidirect
69. C₇×#387	C₂²	semidirect
76. C₇×#386	C₂²	semidirect
85. C₇×#385	C₂²	semidirect
86. C₇×#385	C₂²	semidirect
87. C₇×#385	C₂²	semidirect
88. C₇×#382	C₂²	semidirect
89. C₇×#382	C₂²	semidirect
93. C₇×#380	C₂²	semidirect
94. C₇×#380	C₂²	semidirect
95. C₄×C₇×C₄⋊C₄	C₂²	semidirect
96. C₄×C₇×C₄⋊C₄	C₂²	semidirect
97. C₄×C₇×C₄⋊C₄	C₂²	semidirect
98. C₄×C₇×C₄⋊C₄	C₂²	semidirect
99. C₄×C₇×C₄⋊C₄	C₂²	semidirect
104. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
107. C₂×C₇×#95	C₂²	semidirect
108. #34424	C₇	direct (N × H)
126. C₇×#126	C₂×C₄	semidirect
127. C₇×#124	C₂×C₄	semidirect
128. C₇×#123	C₂×C₄	semidirect
129. C₇×C₂²⋊Q₈	C₂×C₄	semidirect
130. C₇×#121	C₂×C₄	semidirect
131. C₇×#121	C₂×C₄	semidirect
132. C₇×#120	C₂×C₄	semidirect
139. C₄×C₇×D₄	C₂×C₄	semidirect
163. C₂×C₇×C₂²⋊C₄	C₂×C₄	semidirect
218. #2379	C₂×C₇	semidirect
219. #2376	C₂×C₇	semidirect
220. #2367	C₂×C₇	semidirect
221. #2359	C₂×C₇	semidirect
222. #2358	C₂×C₇	semidirect
223. #2358	C₂×C₇	semidirect
224. #2352	C₂×C₇	semidirect
225. #2349	C₂×C₇	semidirect
226. #2334	C₂×C₇	semidirect
227. #2334	C₂×C₇	semidirect
228. #2329	C₂×C₇	semidirect
229. #2325	C₂×C₇	semidirect
230. #2325	C₂×C₇	semidirect
231. #2324	C₂×C₇	semidirect
232. #2315	C₂×C₇	semidirect
233. C₄×C₂²⋊Q₈	C₂×C₇	semidirect
234. C₄×#121	C₂×C₇	semidirect
235. C₂×#388	C₂×C₇	semidirect
360. #538	C₄×C₇	semidirect
368. C₂×C₄×Q₈	C₂²×C₇	semidirect
374. C₂×C₄×D₄	C₂²×C₇	semidirect
375. C₂×#117	C₂²×C₇	semidirect
382. #391	C₂²×C₇	semidirect
383. #391	C₂²×C₇	semidirect
386. #390	C₂²×C₇	semidirect
387. #389	C₂²×C₇	semidirect
388. #389	C₂²×C₇	semidirect
389. #389	C₂²×C₇	semidirect
390. #389	C₂²×C₇	semidirect
391. #389	C₂²×C₇	semidirect
400. #388	C₂²×C₇	semidirect
401. #388	C₂²×C₇	semidirect
402. #388	C₂²×C₇	semidirect
403. #388	C₂²×C₇	semidirect
404. #387	C₂²×C₇	semidirect
405. #387	C₂²×C₇	semidirect
406. #387	C₂²×C₇	semidirect
407. #387	C₂²×C₇	semidirect
408. #387	C₂²×C₇	semidirect
409. #387	C₂²×C₇	semidirect
416. #386	C₂²×C₇	semidirect
425. #385	C₂²×C₇	semidirect
426. #385	C₂²×C₇	semidirect
427. #385	C₂²×C₇	semidirect
428. #382	C₂²×C₇	semidirect
429. #382	C₂²×C₇	semidirect
433. #380	C₂²×C₇	semidirect
434. #380	C₂²×C₇	semidirect
435. C₄×C₄⋊C₄	C₂²×C₇	semidirect
436. C₄×C₄⋊C₄	C₂²×C₇	semidirect
437. C₄×C₄⋊C₄	C₂²×C₇	semidirect
438. C₄×C₄⋊C₄	C₂²×C₇	semidirect
439. C₄×C₄⋊C₄	C₂²×C₇	semidirect
444. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
447. C₂×#95	C₂²×C₇	semidirect
558. #126	C₂×C₄×C₇	semidirect
559. #124	C₂×C₄×C₇	semidirect
560. #123	C₂×C₄×C₇	semidirect
561. C₂²⋊Q₈	C₂×C₄×C₇	semidirect
562. #121	C₂×C₄×C₇	semidirect
563. #121	C₂×C₄×C₇	semidirect
564. #120	C₂×C₄×C₇	semidirect
571. C₄×D₄	C₂×C₄×C₇	semidirect
595. C₂×C₂²⋊C₄	C₂×C₄×C₇	semidirect
921. C₇	#34424	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×#538	2
C₇×#2379	2
C₇×#2376	2
C₇×#2367	2
C₇×#2359	2
C₇×#2358	2
C₇×#2352	2
C₇×#2349	2
C₇×#2334	2
C₇×#2329	2
C₇×#2325	2
C₇×#2324	2
C₇×#2315	2
C₄×C₇×C₂²⋊Q₈	2
C₄×C₇×#121	2
C₂×C₇×#388	2
#34424	7

Subgroups — C7×#34424 #13211640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34424 #13211640